Question: Astrid is in charge of building a new fleet of ships. Each ship requires $40$ tons of wood, and accommodates $300$ sailors. She receives a delivery of $4$ tons of wood each day. The deliveries can continue for $100$ days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least $2100$ sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?
Answer: There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say that Astrid can build $x\,\text{ships}$ if she receives deliveries of wood for the maximum possible number of days, which is $100\,\text{days}$. How can we relate these two quantities with an equation? $\begin{aligned} 100\,\text{days}\cdot y\,\dfrac{\text{ships}}{\text{day}}=x\,\text{ships} \end{aligned}$ So in order to find the number of ships $x$, we need to figure out the value of $y$, which is the rate of ships per day. Notice what other information we are given: $40\,\dfrac{\text{tons}}{\text{ship}}$ $300\,\dfrac{\text{sailors}}{\text{ship}}$ $4\,\dfrac{\text{tons}}{\text{day}}$ $2100\,\text{sailors}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{ships}}{\text{day}}$ ? We can combine the following quantities: $\begin{aligned} &\phantom{=}\dfrac{4\,\dfrac{\text{tons}}{\text{day}}}{40\,\dfrac{\text{tons}}{\text{ship}}} \\\\ &=\dfrac{4}{40}\,\dfrac{\cancel\text{tons}}{\text{day}}\cdot\dfrac{\text{ships}}{\cancel\text{ton}} \\\\ &=0.1\,\dfrac{\text{ships}}{\text{day}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} 100\,\text{days}\cdot 0.1\,\dfrac{\text{ships}}{\text{day}}&=x\,\text{ships} \\\\ 10\,\text{ships}&=x\,\text{ships} \end{aligned}$ In conclusion, assuming Astrid receives the maximum possible amount of wood, she can build $10$ ships.